Subtraction of Directed Numbers by kwanchau

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2013-09-23 21:00

In collections Directed Numbers

This example demonstrates the geometric meaning of directed number subtraction through vector subtraction. It visually shows the result of directed number subtraction. The construction uses point, if, and list commands in GeoGebra. Suitable for middle school and above students to learn the concept and geometric representation of directed number subtraction.

GeoGebra Commands & Parameters

Point(xAxis) → A
Point(xAxis) → B
If(b < 0, Sequence[(a + n, 0), n, 0, -b], Sequence[(a - n, 0), n, 0, b]) → list1
If(a < 0, Sequence[(-n, 0), n, 0, -a], Sequence[(n, 0), n, 0, a]) → list1_2
If(a > 0, Sequence[Semicircle[Element[list1_2, n], Element[list1_2, n + 1]], n, 1, abs(a)], Sequence[Semicircle[Element[list1_2, n + 1], Element[list1_2, n]], n, 1, abs(a)]) → list2_1
If(b > 0, Sequence[Semicircle[Element[list1, n + 1], Element[list1, n]], n, 1, abs(b)], Sequence[Semicircle[Element[list1, n], Element[list1, n + 1]], n, 1, abs(b)]) → list2

AI Drawing Prompt Reference

Draw a geometric representation showing the meaning of directed number subtraction through vector subtraction. Mark two points on the horizontal axis. Generate two sequences of points based on the position of the second point, representing positive and negative directions. Similarly, generate two sequences of points based on the size of the first point. Connect these points with semicircles to form two closed curves, representing the absolute values of the two directed numbers and demonstrating the subtraction geometrically.

The prompt above was compiled from the original drawing commands and is for reference only.